Question

Prove that sum of the angles of a triangle is 180▫.
Q17. Prove that a diagonal of a parallelogram divides it into two congruent triangles.

Answer 1

in a parallelogram sum of all sides is 360 degrees so we can prove that a parallelogram divides into two congruent triangles

Answer 2

Hey Friend, This is your answer of your question.
1. The sum of the angles of a triangle is 180°.
GIVEN : A triangle ABC
TO PROVE: <A + <B + <C
CONSTRUCTION: Through A, draw in line DE parallel to BC.
PROOF : DE||BC and AB is the transversal.
So, <1=<4 (i) (Alt. Int. <s)
Again, DE||BC and AC is the transversal.
So, <2=<5 (ii) (Alt. lnt. <s)
So, <1+<2=<4+<5
[adding the corresponding sides of (i) and (ii) ]
So, <1+<2+<3= <4+<5+<3 [adding <3 on both sides] .
But, <4+<5+<3= <DAE = 180° [ So, <DAE is a straight angle]
So, <1+<2+<3= 180°
Hence, the sum of the angles of a triangle is 180° .